You are inflating a spherical balloon at the rate of 7 cm³/sec. How fast is it radius increasing when the radius is 4cm?

Q: Solve dy Зу - 4х dx x-y – 2x = C 2x* + x-3 y = C 4 x-3y – 2x-2 = C 2x2 + xy = C -3

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Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (E...

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: The deviation of each observation (y) from the mean of the response variable is positive for every p...

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Q: Use Simpson's Rule and n = 4 to find an approximation for the definite integral Vr +1 dr.

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Q: (y+2xy")dx +xdy = 0

A: First order differential equation :           Consider the differential equation                   d...

Q: 1 V3 is a point on the unit circle that corresponds to t, If t is a real number and P = (x, y) = %3D...

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Q: 2 COS os²(5æ) sin*(5æ)dr 4

A: This is a problem of integration. Based on the general formula of integration we will solve the prob...

Q: Find the unit vector having the same direction as v = (1, - 3). %3D 1 3. V 10 V10 10 V10, 3. O (1, 1...

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Q: (y)² = 1-y? 1-x? 2

A: First we take variable separable then integrate it.  Then using given conditions y(1) =1/2 Then we g...

Q: In the answer box below, type an exact answer only (i.e. no decimals). You do not need to fully simp...

A: Given query is to find the indicated half angle trigonometric function.

Q: 3 -dx 4 - x

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Q: Use technology to evaluate the given expression. Take 1.3 7.3 A = 1.6 -2.34 5.7 and B = 5.3 0 O 12.9...

A: A=1.6-2.345.744.9012.9 and B=1.37.35.305.56.3

Q: The nice little graph you see here is the graph of the polar equation r Compute the area enclosed by...

A: Given: - The graph of the polar equation r=sin3θ and the nice little graph is, To find: - The area ...

Q: solve the differential equation   x(4ydx+2xdy)+y3(3ydx+5xdy)=0

A: Given that the differential equation is    x(4ydy+2xdy)+y3(3ydx+5xdy) = 0 

Q: -n ) Σe n=1 1 d) Σ+ 3 п n=1 8

A: C) Given that ∑n=1∞e-n By the integral test, ∫1∞e-x dx=limt→∞∫1te-x dx                              ...

Q: Use a finite sum to estimate the average value of f(x)=x* on [0,2] by partitioning the interval into...

A: To evaluate the f at the subinterval midpoint

Q: sec®(x) dx S V cot(x V cot(x)

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Q: 10. Romeo is walking towards North at a rate of 4m/s. Ten seconds after, Juliet walks towards East a...

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Q: 2. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction...

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Q: f(x+h)-f(x) mplify the difference quotient for the given function f(x) = 7x - 3x+2 x+h) - f(x) (Simp...

A: Per are asked to find the difference quotient 

Q: у (2ху+1) dz +a (1+2ху— г3 у?) dy 3 0 (1+ 2гу— а* у) dy %3D0

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Q: Determine the standard form of equation of a hyperbola with center at (6,4), with a focus at (6, – 1...

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Q: Use the Chain Rule to find the derivative of the function. y (4x2 - 7)3 %3D

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Q: Find the derivative of the function. h(t) = (t5- 1)(312-5t-2) %3D

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Q: In the decomposition a = aTT + aNN, what do aT and aN represent?

A: Solution: Given data, a = aTT + aNN

Q: 2xyy'=1+y^2 solve using separation of variable (diff eq) when y=3 and x=2

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Q: Determine general antiderivatives for each of the following functions (use capital C as the integrat...

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Q: Find the equation of the tangent line to the graph of f(x) = 3x²e*-1 – 1, at ¤ = 1.

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Q: Use Simpson's Rule and n = 4 to find an approximation for the definite integral Vr +1 dr %3!

A: Here, the given function is: f(x)=x3+1 Now, the Simpson's rule formula to approximate the definite i...

Q: 2. S(Vw +2)Vwdx

A: Topic:- integration

Q: 5. csc 4x dx

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Q: Pennstase 2) 2Determine whether the given sequence converges or n2+ 1 ldiverges. If it converges, ca...

A: The objective is to determine whether the given sequence converges or diverges .

Q: х — 3 (x+ 2) (x – 1)²

A: The given integral is; (x-3)/[(x+2)(x-1)2].

Q: 19x? 8x - Evaluate : lim 4x2 + 18

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Q: Determine the standard form of equation of a hyperbola with center at (-2,1), distance from the cent...

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Q: A point (5, 1) on the terminal side of an angle 0 is given. Find the exact value of sec 0. 2/6 3/26 ...

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Q: xy°dx + (y+1) e "dy= 0

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Q: ® 2ly*t9) dx +(1-x*)ydy = %3D

A: given DE 2y2+4dx+1-x2ydy = 02y2+4dx = -1-x2ydy2dx1-x2 = -ydyy2+4integrate on both sides to get the s...

Q: 4. The height h (in metres) of a certain section of a roller coaster is modelled by the equation h(x...

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Q: find mayium. heisht hit)--2+ +8+ t19 which OF descibes LOX 15X5 +3Y-200 the Pollonins accurately He ...

A: We have to find the maximum height using the differenciation

Q: The figure on the right shows the graph of f and a line tangent to the graph of f at x = 7. Find f(7...

A: Given query is to find the value of f(7) and f'(7).

Q: O XsinCyldx +(x^t)cos(y) dy=0

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Q: Find the critical point(s) of the function. S(x. y) = x³y + 12x? – 8y + 1 (Give your answer as a com...

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Q: The least squares equation, y= 18.9476+1.1842x. If y= 66.3156, what is the value of x? *

A: On solving this we will get

Q: Transform the polar equation ?r = 5 cos(0) to an equation in a and y.

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Q: 2x Use substitution to evaluate the integral dx (x² + 3)°

A: We have to apply rules of integration to solve the problem Power rule: xn =( 1/n+1)(x)n-1

Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (E...

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Q: 5. fx6Vex' dx

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Q: If the linear relationship between Y and X is positive (as X increases Y also increases), then there...

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Q: 15 1야 -5 10 /15 -20 -15 -10 20 -5 -10 -150 -20 lim f(x) x--5 -5 lim f(x) 10

A: Topic = limits